A170676 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016

Offset

0,2

Comments

The initial terms coincide with those of A170762, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

Formula

G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +

2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +

2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +

2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +

2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +

2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(861*t^49 - 41*t^48 - 41*t^47 - 41*t^46 - 41*t^45 - 41*t^44 - 41*t^43

- 41*t^42 - 41*t^41 - 41*t^40 - 41*t^39 - 41*t^38 - 41*t^37 - 41*t^36 -

41*t^35 - 41*t^34 - 41*t^33 - 41*t^32 - 41*t^31 - 41*t^30 - 41*t^29 -

41*t^28 - 41*t^27 - 41*t^26 - 41*t^25 - 41*t^24 - 41*t^23 - 41*t^22 -

41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 -

41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 -

41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1)

Mathematica

coxG[{49, 861, -41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 19 2021 *)

Crossrefs

Sequence in context: A170532 A170580 A170628 * A170724 A170762 A218745

Adjacent sequences: A170673 A170674 A170675 * A170677 A170678 A170679

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved